Question with the mode of a pdf

[Andiio]

Say if you had a pdf defined as:

f(x) = {2, -2≤x≤-1.5
          {0, elsewhere

and you wanted to find the mode.

The textbook tells me that no mode exists (which does make sense), but I've also heard from a certain someone that the mode does exist, and each x-coord along the line is effectively the 'mode'. (so wouldn't the mode effectively be = {[-2,-1.5]} ?)

Thanks guys!

[tony3272]

I would have generally said that no mode exists. From my understanding it's just the single value that occurs most frequently, and so it can't be set.
my bad.

[acinod]

There is an infinite number of modes.

[TrueTears]

Say if you had a pdf defined as:

f(x) = {2, -2≤x≤-1.5
          {0, elsewhere

and you wanted to find the mode.

The textbook tells me that no mode exists (which does make sense), but I've also heard from a certain someone that the mode does exist, and each x-coord along the line is effectively the 'mode'. (so wouldn't the mode effectively be = {[-2,-1.5]} ?)

Thanks guys!

http://en.wikipedia.org/wiki/Mode_%28statistics%29#Mode_of_a_probability_distribution

http://en.wikipedia.org/wiki/Maxima_and_minima#Analytical_definition

Thus acinod is right

[Andiio]

Chyeah!

So just wondering, what would be the 'best' way to answer such a question? i.e. providing a formal solution and hence gaining full marks. (from my given example)

Thanks again!

[luken93]

Chyeah!

So just wondering, what would be the 'best' way to answer such a question? i.e. providing a formal solution and hence gaining full marks. (from my given example)

Thanks again!

Mode occurs for x such that f'(x) = 0

Since f'(x) = 0 for all x c [-2, -1.5], x c [-2, -1.5] is the mode.

?

[TrueTears]

Mode occurs for x such that f'(x) = 0

not always, f(x)=x^3

[luken93]

Mode occurs for x such that f'(x) = 0

not always, f(x)=x^3

Dang it! hahaha